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The Design of the New NIST-4 Watt Balance
L.S. Chao, S. Schlamminger, F. Seifert, A. Cao, D. Haddad, D.B. Newell, J.R. Pratt
National Institute of Standards and Technology (NIST)
100 Bureau Drive Stop 8171
Gaithersburg, MD 20899-8171
USA
Email: leon.chao@nist.gov, stephan.schlamminger@nist.gov
Abstract—The design of the new permanent-magnet driven
watt balance and novel mechanical features will demonstrate the
high-precision capabilities of a large complex mass measurement
system with expected overall uncertainties on the order of 3 parts
in 108.
Index Terms—mass, watt balance, kilogram, flexure, perma-
nent magnet
I. INTRODUCTION
A watt balance is a mass measuring apparatus that utilizes a
magnetic field and a movable coil to compare electrical power
to mechanical power. The NIST watt balance experiment
consists of an alternating series of measurement modes called
velocity mode and force mode. This instrument measured one
of the most recent values of the Planck constant in 2013 and
will assist in the realization of the kilogram[2].
NIST-4 is the fourth generation watt balance currently being
built at the National Institute of Standards and Technology.
The most notable change from the previous apparatus is the
shift from a 0.1 Tesla superconducting magnet to a 0.55 Tesla
SmCo permanent magnet system. NIST-4 also has a more
robust design and will be housed inside a 2 m tall vacuum
chamber, significantly smaller than its predecessor which
stands past two stories of a building.
II. NIST-4 COMPONENTS
The NIST-4 watt balance contains only a few key com-
ponents. A monolithic, aluminum spider is suspended and
rotationally decoupled from one side of a diamond-turned
aluminum wheel [Fig. 1]. Next, a copper coil with 885 turns
and a mean diameter of 0.43 m is hung from three identically
paired systems of x-y flexures. The coil is suspended in a
30 mm wide air gap and is allowed to translate vertically +/-
40 mm from its nominal position inside of the magnet system.
A main mass stirrup hangs from the center point of the
spider but pivots independently from the spider and coil assem-
bly. This main mass stirrup serves as the platform for loading
and unloading the main mass and auxiliary mass during force
mode and velocity mode [2]. The 600 mm diameter balance
wheel pivots about a tungsten carbide knife edge linked to
the Extremely Large Flexure (ELF). This monolithic flexure
allows pure translational motion in the x-y directions which is
essential for positioning the coil accurately inside the magnet.
Fig. 1: Drawing of the main components of NIST-4. Vacuum
and support components are omitted.
III. THE MOVING COIL
In velocity mode, the moving coil has six degrees of
freedom given by three components (vx, vy, vz)of its velocity
vand three components (ωx, ωy, ωz)of its angular velocity
Ωabout its center of mass [2]. In force mode, the coil can
generate a force Fwith components (Fx, Fy, Fz)and a torque
Γwith components (τx, τy, τz). Through the combination
of velocity mode and force mode, linked by the magnet
system’s Bl factor, mechanical power is derived and equated
to electrical power [1][2]:
UI =F·v+Γ·Ω(1)
or
UI =Fxvx+Fyvy+Fzvz+τxωx+τyωy+τzωz(2)
Of the twelve variables that contribute to the virtual me-
chanical power, Fzand vzare the only desired components;
all others are deemed as parasitic.
To achieve the precision necessary for realization of mass,
the ratio of each off-axis component to Fzvzmust be min-
imized to a few parts in 10−9(ppb). There are essentially
three ways to accomplish this: (1) diminish the five off-
axis force components, (2) diminish the five off-axis velocity
components, or (3) reduce both the off-axis forces and the
off-axis velocities to diminish the off-axis product F v. For
example, if
Fx
Fz
= 10−4and vx
vz
= 10−5(3)
then, Fxvx
Fzvz
= 10−9(4)
The off-axis X-Y force and torque components are minimized
by concentrically aligning the electrical center of the coil to
the magnetic center of the radial field. By doing this, the
minor magnetic flux gradients cancel on opposing sides of
the coil. Compliancy in the stirrup system, accomplished by
small 2D flexures, allows for monitoring of the parasitic forces
and torques during force mode. However, compliant systems
result in higher amplitude parasitic motions.
IV. HIGH PRECISION ALIGNMENT
In order to achieve the required level of uncertainty for
mass redefinition, the physical alignment of the moving coil’s
electrical center to the field’s magnetic center is important.
These two points must be aligned to one micrometer. However,
the coil’s location traces back to the location of the knife edge,
whose 40 kg load must be precisely positioned with a device
that is both vacuum compatible and non-magnetic.
The ELF was designed and machined from a monolithic
block of 6061-T6 aluminum to adjust the x-y position of the
knife edge and everything attached. The ELF weighs 33 kg,
is 97 cm x 46 cm x 3.8 cm, and has two symmetry planes.
The system contains 24 individual flexures measuring 1.8 mm
wide and 8 mm long. These flexures allow the movement of
the middle plate with respect to the outer ring.
Fig. 2: Top view of the ELF. Pushing on the tabs indicated
by the arrows result in X and Y displacements of the middle
plate. Desired displacements = +/- 0.5 mm in X and Y.
The symmetric design and the collinear flexures are sig-
nificant in removing off-axis motions, preserving pure linear
motion in X and Y. Focusing only on the lower left quadrant,
three collinear flexures are apparent. Pushing on the bottom
actuation flexure in the +y direction pivots the whole beam
about the fulcrum flexure, resulting in a pulling force applied
to the tensile flexure and displacement of the middle plate in
the -y direction. The same is conducted with the outer flexures
for displacements in the x direction.
V. AUXILIARY MASS
When switching between velocity mode and force mode in
the existing watt balance, a 1
2kg counter mass is loaded and
unloaded from the mass pan hanging from the far side of the
wheel. A design flaw is exposed during this process: the knife
edge experiences a 1 kg heavier load in force mode than in
velocity mode, affecting the hysteresis in the knife edge.
Existing Watt Balance
Mode F M A = C Knife Load
Velocity 0 0 0 = 0 0
Force (Moff ) 5 N 0 0 = 5 N 10 N
Force (Mon) -5 N 10 N 0 = 5 N 10 N
NIST-4
Mode F M A = C Knife Load
Velocity 0 0 5 N = 5 N 10 N
Force (Moff ) 5 N 0 0 = 5 N 10 N
Force (Mon) -5 N 10 N 0 = 5 N 10 N
TABLE I: A comparison between the knife edge load in
the existing watt balance and NIST-4: For NIST-4, a 5 N
auxiliary mass (A) is inserted during velocity mode to maintain
consistency between the 5 N coil force (F) and the 10 N main
mass (M) during force mode. Force mode is comprised of a
series of main mass insertions and removals (Mon and Moff).
The counter mass (C) on the far side of the balance wheel
becomes a fixed 5 N tare mass.
To remedy this issue for NIST-4, the counter mass was
replaced with a 1
2kg fixed tare mass. A 1
2kg auxiliary mass
was introduced to the main mass side to serve as the new
counter mass. Using its own on/off system, the auxiliary mass
is removed from the system during force mode and reinserted
during velocity mode as a novel way to balance the wheel.
VI. CONCLUSION
NIST-4 will be used to realize the kilogram once the redef-
inition of the SI has occurred with expected uncertainties of
3 parts in 108. To disseminate mass with similar uncertainties
demands high precision mechanical components capable of
sub-micron repeatability and accuracy.
REFERENCES
[1] I.A. Robinson, Alignment of the NPL Mark II Watt Balance, Meas. Sci.
Technol. 23, November 2012.
[2] S. Schlamminger, et al. Determination of the Planck constant using a watt
balance with a superconducting magnet system at the National Institute
of Standards and Technology, submitted to Metrologia.
